A camera store sells 40 pairs of binoculars per week on average with a standard deviation of 6. What is the probability that the store will sell more than 52 pairs binoculars in any week?
8.28
3.57
7.24
2.28
4.55
oops - all those "probabilities" are > 1
is there a mistake in the question?
no all the answer choices are percentages
52 is 2 std from 40, so 2.28%
thank you
A camera store sells 40 pairs of binoculars per week on average with a standard deviation of 6. What is the probability that the store will sell more than 52 pairs binoculars in any week?
To find the probability that the store will sell more than 52 pairs of binoculars in any given week, we need to use the concept of the standard normal distribution.
First, let's determine the z-score for 52 pairs of binoculars. The z-score measures how many standard deviations a particular value is from the mean.
z = (X - μ) / σ
where X is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.
In this case, X = 52, μ = 40, and σ = 6.
z = (52 - 40) / 6
z = 12 / 6
z = 2
Next, we need to find the probability associated with this z-score using a standard normal distribution table or a calculator. The probability of getting a z-score of 2 or higher represents the probability that the store will sell more than 52 pairs of binoculars.
Referring to a standard normal distribution table or using a calculator, we find that the probability associated with a z-score of 2 is approximately 0.9772.
Therefore, the probability that the store will sell more than 52 pairs of binoculars in any given week is approximately 0.9772.
So, option 2.28 is the correct answer.